Same thing happens on my Fet Valve Ultra 550. It stays on a good while, maybe 10-15 sec or so before it finally fades away completely. I assume that some power is kept in "reservoir" somewhere in the system and its just draining out on power off.
The use of the word "reservoir" is appropriate. The "reservoir" is the power supply filter capacitors. Under normal operation, they take a full-wave rectified voltage signal that looks like a series of bumps, where the voltage in jumping up and down at 120 hz. but spending most of the time near the peak. The capacitors stores some energy on the way up, and then release it as the voltage goes down. This fills in the low spots between bumps. The net effect is to smooth out the voltage signal and make it a clean and more-or-less constant voltage. To simplify it, the larger these capacitors are, the smoother this voltage will be. Take them out, and it would probably still play but there would likely be a 120 hz hum. On a 300 watts/channel amplifier, they are quite large (since the more power you supply to the speakers, the faster the voltage will decay between bumps, everything else being equal). When you turn off the power, the charging voltage goes away but the capacitor have stored a pretty good bit of energy, which then keeps it going for some amount of time while the capacitor voltage decays away. You can see how well it must be working as a filter - if it keeps playing for 10 seconds, imagine how little it must decay in 1/120hs of a second between bumps.
Used to be that everybody put in the biggest power supply capacitors you could fit in the box, and in some cases there were external cap boxes to get around the space issue. They looked like Campbell's soup cans in terms of size. I think most people have clued in to the idea that this may not be ideal.
Power supply capacitors are usually the life-limiting item in many cases. I repair old radios and vintage hi-fi equipment and I usually won't power up the radio until I have replaced them.
Brett